Stark points and the Hida–Rankin p-adic L-function

Multivariate P-adic L-function

In the recent, many mathematicians studied the multiple zeta function in the complex number field. In this paper we construct the p-adic analogue of multiple zeta function which interpolates the generalized multiple Bernoulli numbers attached to χ at negative integers. §1. Introduction Let p be a fixed prime. Throughout this paper Z p , Q p , C and C p will, respectively, denote the ring of p-a...

The “missing” p-adic L-function – DRAFT

STARK POINTS AND p-ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE

Let E be an elliptic curve over Q, and let %[ and %] be odd two-dimensional Artin representations for which %[ ⊗ %] is self-dual. The progress on modularity achieved in recent decades ensures the existence of normalized eigenforms f , g, and h of respective weights two, one, and one, giving rise to E , %[, and %] via the constructions of Eichler and Shimura, and of Deligne and Serre. This artic...

Integral and p-adic Refinements of the Abelian Stark Conjecture

We give a formulation of the abelian case of Stark’s Main Conjecture in terms of determinants of projective modules and briefly show how this formulation leads naturally to its Equivariant Tamagawa Number Conjecture (ETNC) – type integral refinements. We discuss the Rubin-Stark integral refinement of an idempotent p1 iece of Stark’s Abelian Main Conjecture. In the process, we give a new formula...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES